A study of accurate exchange-correlation functionals through adiabatic connection

TL;DR

This paper evaluates the accuracy of various exchange-correlation functionals in density functional theory by analyzing their performance in reproducing energies under scaled electron-electron interactions, providing insights into their reliability.

Contribution

It introduces a comparative analysis of GGA, hybrid, and meta-GGA functionals using a novel scaling approach to assess their accuracy in exchange-correlation energy calculations.

Findings

SCAN functional satisfies multiple known constraints.

Hybrid functionals B3LYP and PBE0 show different accuracy levels.

Differences in kinetic energy between interacting and non-interacting systems are highlighted.

Abstract

A systematic way of improving exchange-correlation energy functionals of density functional theory has been to make them satisfy more and more exact relations. Starting from the initial GGA functionals, this has culminated into the recently proposed SCAN(Strongly constrained and appropriately normed) functional that satisfies several known constraints and is appropriately normed. The ultimate test for the functionals developed is the accuracy of energy calculated by employing them. In this paper, we test these exchange-correlation functionals -the GGA hybrid functionals B3LYP and PBE0, and the meta-GGA functional SCAN- from a different perspective. We study how accurately these functionals reproduce the exchange-correlation energy when electron-electron interaction is scaled as scaling parameter times Vee with this parameter varying between 0 and 1. Our study reveals interesting comparison between these functionals and the associated difference Tc between the interacting and the non-interacting kinetic energy for the same density.